We find that, under the assumption of non-satiation with respect to teams for every agent, an extension of the simple notion of pair-wise stability ([1]}) to this setup – which we call myopic team-wise stability – does not have a strong predictive power on the stable states of the model; in particular, feasible states that are maximal with respect to set inclusion are myopically team-wise stable.
Therefore, we compare two possible refinements.
The first,  following the same approach of [2]}, is given by stochastic stability: in the presence of extremely rare errors that can create or dissolve teams, and with agents that adapt myopically to the current state of the system, we find that the stochastically stable states are those that actually maximize the overall number of teams.
The second is a generalization of coalitional stability for cooperative games ([3]}): its predictive capability will turn out to be heavily dependent on the assumptions on payoff functions.
Moreover, when all projects are equivalent for every agent in terms of costs (resources employed) and benefits (payoffs earned), we find that the states that satisfy this form of coalitional stability are exactly the same as those that are myopically team-wise stable.
Therefore, this latter refinement – which is much more demanding in terms of agents' rationality – proves to have no greater predictive power with respect to myopic team-wise stability in a stark but significant case.
